It is expected by utilizing the Faraday effect of an optical fiber to realize a current sensor (optical fiber current sensor) which has various advantages such as a small size, a flexibility, an electromagnetic noise immunity, a long-distance signal transmission and a withstand voltage. Therefore, the researches and developments of optical fiber current sensors have been carried forward over a long term of years by many institutions. Among them, as a typical developed example, there is a scheme characterized in that a lead glass fiber is employed for a sensor fiber and that a mirror is arranged at one end of the sensor fiber, that is, a lead glass fiber photocurrent sensor of reflection type as disclosed in Patent Document 1.
The configuration of the device disclosed in Patent Document 1 is shown in FIG. 18. Referring to the figure, numeral 1 designates a light source, numeral 11 a circulator, numeral 12 a polarizing separation element of calcite or the like, numeral 13 a ferromagnetic Faraday rotor which consists of a permanent magnet (13a) and a ferromagnetic crystal (13b) of YIG or the like, numeral 14 a mirror, numeral 15 an electric conductor through which a current to-be-measured flows, numeral 16 a sensor fiber, signs 21A and 21B light receiving elements (PD's), signs 22A and 22B amplifiers (A's), signs 23A and 23B band-pass filters (BPF's), signs 24A and 24B low-pass filters (LPF's), signs 25A and 25B dividers for calculating the ratios between the AC components and DC components of electric signals, numeral 26 a polarity inverter, and numeral 27 a multiplier. Incidentally, numeral 10 designates an optical system, numeral 20 designates a signal processing circuit, and the circulator 11 can be replaced with a semitransparent mirror or an optical fiber coupler. As the sensor fiber 16, a lead glass fiber is employed here, but a silica glass fiber can also be employed.
A polarized state in and around the polarizing separation element in FIG. 18 is as shown in FIG. 19. Here, an x-direction shall indicate a direction perpendicular to the sheet of the drawing, and a y-direction a direction parallel to the sheet of the drawing.
As shown in FIG. 19, in light guided from the light source 1 and entering the polarizing separation element 12, a component E1(●) (a vector quantity is indicated by assigning a dot) which oscillates in the x-direction passes through the polarizing separation element 12, and it thereafter enters the sensor fiber 16. Next, E2(●) is let denote the polarized wave of light which is reflected from the mirror 14, which passes through the sensor fiber 16 and the ferromagnetic Faraday rotor 13 again and which returns to the polarizing separation element 12.
The polarized wave is rotated when it passes through the ferromagnetic Faraday rotor (13) and the sensor fiber (16), so that both an x-directional component and a y-directional component arise as shown in FIG. 20 in the component E2(●), and it is understood that the polarization components EA and EB which are separated into two are expressed as the following formulas:EA=EM cos(2θG+2θi)cos ω1t EB=EM sin(2θG+2θi)cos ω1t 
Here,    EM: amplitude (V/m) of the return light E2(●),    ω1: angular frequency (rad/sec) of the light wave,    θG: Faraday rotation angle (rad) which the light passing through the ferromagnetic Faraday rotor once undergoes, and accordingly, the rotation angle becomes 2θG in the case where the light reciprocates,    θi: rotation angle (Faraday rotation angle) (rad) of the polarized wave based on a Faraday effect which the light undergoes when passing through the sensor fiber once, and accordingly, the rotation angle becomes 2θi in the case where the light reciprocates.
Here, the intensity of the light is proportional to the temporal mean value of the square of the instantaneous value of the oscillation of the polarized wave, and hence, the intensities IA and IB of the respective polarized waves EA and EB become as indicated by formulas given below. Incidentally, mean values are indicated by assigning (−) to signs.
                              I          A                =                              k            1                    ⁢                      {                                          E                M                2                            ⁢                                                cos                  2                                ⁡                                  (                                                            2                      ⁢                                              θ                        G                                                              +                                          2                      ⁢                                              θ                        i                                                                              )                                            ⁢                              cos                2                            ⁢                              ω                1                            ⁢              t                        }                    ⁢                      (            -            )                                                            =                                    (                              1                /                4                            )                        ⁢                          k              1                        ⁢                          E              M              2                        ⁢                          {                              1                +                                  cos                  ⁢                                                                          ⁢                  4                  ⁢                                      (                                                                  θ                        G                                            +                                              θ                        i                                                              )                                                              }                                      ⁢                                  ⁢                                  ⁢                  Likewise          ,                                                  I                                                            ⁢            B                          =                              k            1                    ⁢                      {                                          E                M                2                            ⁢                                                sin                  2                                ⁢                                  (                                                            2                      ⁢                                              θ                        G                                                              +                                          2                      ⁢                                              θ                        i                                                                              )                                            ⁢                              cos                2                            ⁢                              ω                1                            ⁢              t                        }                    ⁢                      (            -            )                                                  =                              (                          1              /              4                        )                    ⁢                      k            1                    ⁢                      E            M            2                    ⁢                      {                          1              -                              cos                ⁢                                                                  ⁢                4                ⁢                                  (                                                            θ                      G                                        +                                          θ                      i                                                        )                                                      }                              Here,    {*} (−): temporal mean    IA: intensity (W/m2) of the component A passing through the polarizing separation element,    IB: intensity (W/m2) of the component B passing through the polarizing separation element,    k1: coefficient.
The respective lights indicated by the above intensities IA and IB are guided to the light receiving elements PDA and PDB by the circulator (11) and the polarizing separation element (12) in FIG. 18, and currents or voltages which are proportional to the intensities IA and IB of the received lights are outputted as signals from the light receiving elements. These electric signals pass through the amplifiers 22A and 22B, and thereafter become electric signals PA and PB shown in FIG. 18. These are expressed as the following formulas:
                                                                        P                A                            =                              A                ·                                                      cos                                          2                      ⁢                                                                                                                            ⁡                                      (                                                                  2                        ⁢                                                  θ                          G                                                                    +                                              2                        ⁢                                                  θ                          i                                                                                      )                                                                                                                          =                              A                ⁡                                  [                                      1                    +                                          cos                      ⁢                                              {                                                  4                          ⁢                                                      (                                                                                          θ                                g                                                            +                                                              θ                                i                                                                                      )                                                                          }                                                                              ]                                                                                        (                  1          ⁢          a                )                                          P          B                =                  B          ⁡                      [                          1              -                              cos                ⁢                                  {                                      4                    ⁢                                          (                                                                        θ                          G                                                +                                                  θ                          i                                                                    )                                                        }                                                      ]                                              (                  1          ⁢          b                )            
Here, both “A” and “B” are coefficients which are proportional to mean received light quantities, and they change with the power of the light source, the fluctuations of the attenuations of the lights in optical paths which extend from the light source to the light receiving elements (21's), and so forth. “θG” and “θi” are the rotation angles (Faraday rotation angles) of the polarization planes as stated above.
Besides, since the current to-be-measured is the AC current,θi=V i  (2a)i=I0 cos ωt  (2b)θi=V I0 cos ωt  (2c)hold. Here,    V: Verdet constant (rad/A) of the sensor fiber,    i: current to-be-measured (A),    I0: amplitude (A) of the current to-be-measured,    ω: angular frequency (rad/sec) of the current to-be-measured.
Now, it will be considered that the Verdet constant V of the sensor fiber and the Faraday rotation angle θG depend upon temperatures.
More specifically,V=(1+αT)Vs  (3)θG=(1+βT)Fsd  (4)are assumed. Here,    Vs: Verdet constant (rad/A) of the sensor fiber at a reference temperature,    α: temperature-dependence coefficient (1/° C.) of the Verdet constant of the sensor fiber (for example, the coefficient α of the lead glass fiber is on the order of 0.01%/K, the coefficient α of the silica glass fiber is on the order of 0.0069%/K),    T: difference (° C.) between the ambient temperature of the sensor and the reference temperature,    Fs: Faraday rotatability (rad/m) of the ferromagnetic Faraday rotor at the reference temperature,    d: thickness of the ferromagnetic Faraday rotor (m),    β: temperature-dependence coefficient (1/° C.) of the Faraday rotatability of the ferromagnetic Faraday rotor.
Besides, in order to ensure the linearity of the input/output characteristic of the sensor, an optical bias is obtained as indicated by the following formula:Fsd=π/8  (5a)Incidentally,θGs=Fs d  (5b)holds. Here,    θGs: Faraday rotation angle (rad) which the light passing through the ferromagnetic Faraday rotor undergoes at the reference temperature.
When Formulas (2), (3), (4) and (5) are substituted into the foregoing formulas (1), the formulas of the electric signals PA and PB in which the temperature dependences of the constituent components are considered are obtained:
                                                                        P                A                            =                              A                ⁡                                  [                                      1                    +                                          cos                      ⁢                                              {                                                                              4                            ⁢                                                          (                                                              1                                +                                                                  β                                  ⁢                                                                                                                                          ⁢                                  T                                                                                            )                                                        ⁢                                                          F                              s                                                        ⁢                            d                                                    +                                                                                    (                                                              1                                +                                                                  α                                  ⁢                                                                                                                                          ⁢                                  T                                                                                            )                                                        ⁢                                                          V                              s                                                        ⁢                                                          I                              0                                                        ⁢                            cos                            ⁢                                                                                                                  ⁢                            ω                            ⁢                                                                                                                  ⁢                            t                                                                          }                                                                              ]                                                                                                        =                              A                ⁡                                  [                                      1                    +                                          cos                      ⁢                                                                                          ⁢                                              {                                                                              π                            /                            2                                                    +                                                      4                            ⁢                                                                                                                  ⁢                            β                            ⁢                                                                                                                  ⁢                                                          f                              s                                                        ⁢                            d                            ⁢                                                                                                                  ⁢                            T                                                    +                                                      4                            ⁢                                                          (                                                              1                                +                                                                  α                                  ⁢                                                                                                                                          ⁢                                  T                                                                                            )                                                        ⁢                                                          V                              s                                                        ⁢                                                          I                              0                                                        ⁢                            cos                            ⁢                                                                                                                  ⁢                            ω                            ⁢                                                                                                                  ⁢                            t                                                                          }                                                                              ]                                                                                        (                  6          ⁢          a                )                                          P          B                =                  B          ⁡                      [                          1              -                              cos                ⁢                                  {                                                            π                      /                      2                                        +                                          4                      ⁢                                                                                          ⁢                      β                      ⁢                                                                                          ⁢                                              f                        s                                            ⁢                      d                      ⁢                                                                                          ⁢                      T                                        +                                          4                      ⁢                                              (                                                  1                          +                                                      α                            ⁢                                                                                                                  ⁢                            T                                                                          )                                            ⁢                                              V                        s                                            ⁢                                              I                        0                                            ⁢                      cos                      ⁢                                                                                          ⁢                      ω                      ⁢                                                                                          ⁢                      t                                                        }                                                      ]                                              (                  6          ⁢          b                )            
Here, the following is assumed as conditions which actually hold:|4βFsd T|<<π/2  (7a)|4(1+αT)VsI0|<<π/2  (7b)
When Formulas (7a) and (7b) are substituted into Formulas (6), Formulas (6) become the following formulas:
                                                                        P                A                            =                              A                ⁢                                  {                                      1                    -                                          sin                      ⁢                                                                                          ⁢                      4                      ⁢                                              (                                                  β                          ⁢                                                                                                          ⁢                                                      F                            s                                                    ⁢                          d                          ⁢                                                                                                          ⁢                          T                                                )                                                              +                                          4                      ⁢                                              (                                                  1                          +                                                      α                            ⁢                                                                                                                  ⁢                            T                                                                          )                                            ⁢                                              V                        s                                            ⁢                                              I                        0                                            ⁢                      cos                      ⁢                                                                                          ⁢                      ω                      ⁢                                                                                          ⁢                      t                                                        }                                                                                                        =                              A                ⁢                                  {                                                            (                                              1                        -                                                  4                          ⁢                                                                                                          ⁢                          β                          ⁢                                                                                                          ⁢                                                      F                            s                                                    ⁢                          d                          ⁢                                                                                                          ⁢                          T                                                                    )                                        -                                          4                      ⁢                                              (                                                  1                          +                                                      α                            ⁢                                                                                                                  ⁢                            T                                                                          )                                            ⁢                                              V                        s                                            ⁢                                              I                        0                                            ⁢                      cos                      ⁢                                                                                          ⁢                      ω                      ⁢                                                                                          ⁢                      t                                                        }                                                                                        (                  8          ⁢          a                )                                          P          B                =                  B          ⁢                      {                                          (                                  1                  +                                      4                    ⁢                    β                    ⁢                                                                                  ⁢                                          F                      s                                        ⁢                    d                    ⁢                                                                                  ⁢                    T                                                  )                            +                              4                ⁢                                  (                                      1                    +                                          α                      ⁢                                                                                          ⁢                      T                                                        )                                ⁢                                  V                  s                                ⁢                                  I                  0                                ⁢                cos                ⁢                                                                  ⁢                ω                ⁢                                                                  ⁢                t                                      }                                              (                  8          ⁢          b                )            
The first terms of Formulas (8a) and (8b) are the DC components of the signals. Besides, the second terms are the AC components. These fluctuate with temperatures. Accordingly, modulation signals SA and SB in FIG. 18 are the ratios between the DC components and AC components of the electric signals PA and PB and indicate modulation degrees. These signals can be expressed as the following formulas, considering the fact that the AC components and DC components of the electric signals are separated by the BPF's and LPF's, the fact that the signal SA has had its polarity inverted, and the condition of Formula (7a):
                                                                        S                A                            =                                                                                          (                                              -                        1                                            )                                        ⁡                                          [                                              P                        A                                            ]                                                                            A                    ⁢                                                                                  ⁢                    C                                                  /                                                      [                                          P                      A                                        ]                                                        D                    ⁢                                                                                  ⁢                    C                                                                                                                          =                                                -                  1                                ×                                                      {                                                                  -                        4                                            ⁢                                              (                                                  1                          +                                                      α                            ⁢                                                                                                                  ⁢                            T                                                                          )                                            ⁢                                              V                        s                                            ⁢                                              I                        0                                            ⁢                      cos                      ⁢                                                                                          ⁢                      ω                      ⁢                                                                                          ⁢                      t                                        }                                    /                                      (                                          1                      -                                              4                        ⁢                                                                                                  ⁢                        β                        ⁢                                                                                                  ⁢                                                  F                          s                                                ⁢                        d                        ⁢                                                                                                  ⁢                        T                                                              )                                                                                                                          =                                                                    (                                          1                      +                                              α                        ⁢                                                                                                  ⁢                        T                                                              )                                    ·                  4                                ⁢                                  V                  s                                ⁢                                  I                                      0                    ⁢                                                                                                                ⁢                cos                ⁢                                                                  ⁢                                  ωt                  /                                      (                                          1                      -                                              4                        ⁢                                                                                                  ⁢                        β                        ⁢                                                                                                  ⁢                                                  F                          s                                                ⁢                        d                        ⁢                                                                                                  ⁢                        T                                                              )                                                                                                          (                  9          ⁢          a                )                                                                                    S                B                            =                                                                    [                                          P                      B                                        ]                                                        A                    ⁢                                                                                  ⁢                    C                                                  /                                                      [                                          P                      B                                        ]                                                        D                    ⁢                                                                                  ⁢                    C                                                                                                                          =                                                                    (                                          1                      +                                              α                        ⁢                                                                                                  ⁢                        T                                                              )                                    ·                  4                                ⁢                                                                  ⁢                                  V                  s                                ⁢                                  I                  0                                ⁢                cos                ⁢                                                                  ⁢                ω                ⁢                                                                  ⁢                                  t                  /                                      (                                          1                      +                                              4                        ⁢                                                                                                  ⁢                        β                        ⁢                                                                                                  ⁢                                                  F                          s                                                ⁢                        d                        ⁢                                                                                                  ⁢                        T                                                              )                                                                                                          (                  9          ⁢          b                )            
Further, from Formulas (9), a final output Sout in FIG. 18 becomes:
                                                                        S                out                            =                                                (                                                            S                      A                                        +                                          S                      B                                                        )                                /                2                                                                                        =                                                (                                      1                    /                    2                                    )                                ⁢                                                                  ⁢                                  {                                                            1                      /                                              (                                                  1                          -                                                      4                            ⁢                                                                                                                  ⁢                            β                            ⁢                                                                                                                  ⁢                                                          F                                                              s                                ⁢                                                                                                                                                                                        ⁢                            d                            ⁢                                                                                                                  ⁢                            T                                                                          )                                                              +                                          1                      /                                              (                                                  1                          +                                                      4                            ⁢                                                                                                                  ⁢                            β                            ⁢                                                                                                                  ⁢                                                          F                              s                                                        ⁢                            d                            ⁢                                                                                                                  ⁢                            T                            ×                                                                                                                                                                                                                      =                              4                ⁢                                  (                                      1                    +                                          α                      ⁢                                                                                          ⁢                      T                                                        )                                ⁢                                  V                  s                                ⁢                                  I                  0                                ⁢                cos                ⁢                                                                  ⁢                ω                ⁢                                                                  ⁢                t                                                                                        =                                                                    (                                          1                      +                                              α                        ⁢                                                                                                  ⁢                        T                                                              )                                    ·                  4                                ⁢                                  V                  s                                ⁢                                  I                  0                                ⁢                cos                ⁢                                                                  ⁢                ω                ⁢                                                                  ⁢                                  t                  /                                      {                                                                  (                                                  1                          -                                                      4                            ⁢                                                                                                                  ⁢                            β                            ⁢                                                                                                                  ⁢                                                          F                              s                                                        ⁢                            d                            ⁢                                                                                                                  ⁢                            T                                                                          )                                            ·                                                                                                                                                              =                                  (                                      1                    +                                          4                      ⁢                                                                                          ⁢                      β                      ⁢                                                                                          ⁢                                              F                        s                                            ⁢                      d                      ⁢                                                                                          ⁢                      T                                                        )                                            }                                                                          =                                                                    (                                          1                      +                                              α                        ⁢                                                                                                  ⁢                        T                                                              )                                    ·                  4                                ⁢                                                                  ⁢                                  V                  s                                ⁢                                  I                  0                                ⁢                cos                ⁢                                                                  ⁢                ω                ⁢                                                                  ⁢                                  t                  /                                      {                                          1                      -                                                                        (                                                      4                            ⁢                            β                            ⁢                                                                                                                  ⁢                                                          F                              s                                                        ⁢                            d                            ⁢                                                                                                                  ⁢                            T                                                    )                                                2                                                              }                                                                                                          (        10        )            
When the quadratic term of the denominator of Formula (10) is omitted in consideration of the condition of the above formula (7a), the output Sout is roughly expressed by the following formula:Sout≈(1+αT)●4VsI0 cos ωt  (11)
The current measurement device which measures such a current to-be-measured i indicated in the current measurement device shown in FIG. 18 has the following advantages:    1) The device is not influenced by the fluctuations of the mean received light quantities.
As understood from Formulas (9a) and (9b), those coefficients A and B of Formulas (6a) and (6b) which are measurement errors arising from the vibrations of the light source, etc. are eliminated by calculating the modulation signals SA and SB.    2) The device is not influenced by a photoelasticity.
Although no description has been made in terms of formulas, the lead glass fiber is employed for the sensor fiber, whereby the device does not undergo output fluctuations ascribable to the stress of the sensor fiber.    3) The device is not influenced by the deformation of a curve which the sensor fiber forms.
Although no description has been made in terms of formulas, the device is configured as the reflection type, whereby the polarized wave of the emergent light from the fiber does not depend upon a curve shape.    4) The device can suppress the temperature fluctuations of the optical bias.
As understood from Formulas (9)-(11), the influence which is exerted on the output Sout by the temperature dependence of the Faraday rotatability of the ferromagnetic Faraday rotor can be relieved by calculating the mean of the two modulation signals SA and SB.
The merits 1)-3) are expressed in other words, as follows:    1) The device is stable against the fluctuations of the light emission quantity of the light source and the connection efficiency of the optical system.    2) and 3) A frame for fixing the sensor fiber is dispensed with, and the whole sensor becomes small-sized and flexible. Besides, the sensor can be attached without opening the conductor through which the current to-be-measured flows.
Incidentally, the advantages etc. of the current measurement device shown in FIG. 18 are detailed in, for example, Document 1 and Patent Document 1.    Document 1: Kurosawa, Hiroki and Shirakawa, “Small-sized and Flexible Optical fiber current sensor”, Collection of Papers of Lectures in the 30th Meeting of the Society for the Research of Light Wave Sensing Technology, P. 133-140, No. LST30-19, December 2002    Patent Document 1: JP-A-10-319051